Harmonic Generation in Low-Field Nuclear Induction

Abstract

The generation of second harmonics has been observed in a low-field nuclear-induction experiment with nearly coincident, constant and alternating, magnetic fields. A pair of Helmholtz coils furnishes both a constant (H0) and an alternating (amplitude ηH0) magnetic field, and a second Helmholtz pair furnishes a constant, small magnitude (hH0) field perpendicular to the first pair. Steady-state solutions of the modified Bloch equations (relaxation to the instantaneous field) that utilize the indicated field configuration (obtained by both analytic and numerical methods) indicate first, the existence of resonance when ωR, the alternating field frequency, is a subharmonic of the gyromagnetic frequency ω0(≡γH0), and, second, relatively slow variation of the magnetic-moment components as functions of η. Analysis and experiment indicate saturation of the signal with increasing h. The nuclear sample, water with a heavy concentration of Cu(NO3)2·3H2O, about 3 cm in diameter, was closely surrounded by a 1000-turn pickup coil the output of which was fed to a narrowband wave analyzer tuned to 2ωR. With H0=6.11 G, η=2, and h=0.013, the predicted and observed second-harmonic (52 kc/sec) voltage was 0.1 μV (rms).